5. Monopoly Supplier of Non-renewable Resource Assume you operate the only oil well in a world with only two periods (q, and q2). The stock of oil in ground under your

well is 100 barrels. You have a discount rate of .1 and have an oil extraction cost function: c(Qc) = 25+ 8Q, +2Q² There is the consumer demand function: Qt = 100-2pt Therefore, the monopolist supplier determining the supply of oil will receive the price: Qt Pt = 50 a. Set up the problem using a Lagrange multiplier framework. b. Derive the first order conditions which must hold for the optimum. c. Solve for the optimal monopolist quantities and prices of oil to be extracted.